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07 Dec 2012, 08:30
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On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?
(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.
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Number line.png [ 2.33 KiB | Viewed 79093 times ]
07 Dec 2012, 08:37
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On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?
{p, q, r, s, t} is an evenly spaced set thus its mean = median = middle term = r.
(1) q + s =24. Since q, r and s are consecutive even integers, then q=r-2 and s=r+2 --> (r-2)+(r+2)=24 --> r=12. Sufficient.
(2) The average (arithmetic mean) of q and r is 11. (r-2)+r=2*11 --> r=12. Sufficient.
Answer: D.
24 Feb 2015, 22:38
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Hi All,
This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.
We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.
Fact 1: Q + S = 24
Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....
IF Q, R and S are....
2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)
IF Q, R and S are a bit bigger, say....
8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...
IF Q, R and S are....
10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).
By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits.
Fact 1 is SUFFICIENT.
Fact 2: The average of Q and R is 11
Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....
IF Q and R are....
8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)
IF Q and R are...
10 and 12, then the average is 11. This is a MATCH.
Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.
We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.
Fact 1: Q + S = 24
Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....
IF Q, R and S are....
2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)
IF Q, R and S are a bit bigger, say....
8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...
IF Q, R and S are....
10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).
By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits.
Fact 1 is SUFFICIENT.
Fact 2: The average of Q and R is 11
Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....
IF Q and R are....
8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)
IF Q and R are...
10 and 12, then the average is 11. This is a MATCH.
Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
